Differential Equations

5 solved problems from JEE previous year papers.

Differential Equations

If the Integral of t·f(t) From 0 to x Equals x²·f(x) and f(2) = 3, Then f(6) Equals

JEE Main 2025 PYQ: if ∫₀ˣ t·f(t)dt = x²·f(x) and f(2)=3, find f(6) by differentiating both sides to form and solve a differential…
Differential Equations

For Any Real Numbers α and β, Let y(α,β)(x) Be the Solution of dy/dx + αy = xe^(βx), y(1) = 1. If S = {y(α,β)(x) : α, β ∈ R}, Then Which of the Following Functions Belong to S

For real α, β let y_{α,β}(x) solve dy/dx+αy=xe^(βx), y(1)=1. S is the set of all such functions. Which given options belong to S?…
Differential Equations

Let the Solution Curve y = y(x) of dy/dx − 3x⁵tan⁻¹(x³)y/(1+x⁶)^(3/2) = 2x·exp((x³−tan⁻¹x³)/√(1+x⁶)) Pass Through the Origin. Then y(1) Is Equal To

The solution curve y=y(x) of dy/dx − 3x⁵tan⁻¹(x³)y/(1+x⁶)^(3/2) = 2x·exp[(x³−tan⁻¹x³)/√(1+x⁶)] passes through the origin. Find…
AIEEE 2010

The Solution of the Differential Equation cos x·dy = y(sin x − y)dx, for 0 < x < π/2, Is

Solve the differential equation cos x dy = y(sin x − y)dx for x in (0,π/2), by recognising it as a Bernoulli equation and…
Differential Equations

y=(x−y dx/dy)sin(x/y), x(1)=π/2 — Find cos(x(2))

Solve the differential equation y=(x−y dx/dy)sin(x/y) with x(1)=π/2, using the substitution v=x/y to reduce it to a separable…